A number of experiments provide evidence supporting the existence of topological phases of matter with non-Abelian anyonic quasiparticles. Ising-type σ nonAbelian anyons occur as quasiparticles in a number of quantum Hall states that are strong candidates for describing experimentally observed quantum Hall plateaus in the second Landau level, most notably for the v=5/2 plateau, which has experimental evidence favoring a non-Abelian state. Ising anyons also describe the Majorana fermion zero modes (MZMs) which exist in vortex cores of two-dimensional (2D) chiral p-wave superfluids and superconductors, at the ends of Majorana nanowires (one-dimensional spinless, p-wave superconductors), and quasiparticles in various proposed superconductor heterostructures. Recent experiments in superconductor/semiconductor nanowire heterostructure systems have found evidence of MZMs and hence realization of Majorana.
Non-Abelian anyonic quasiparticles may be used to provide topologically protected qubits and quantum information processing. Schemes for implementing fusion, (braiding) exchange operations, and topological charge measurements of non-Abelian quasiparticles have previously been disclosed.
In systems with Ising-type anyons/MZMs, quasiparticle exchange and topological charge measurement allow these systems to be used for topological quantum information processing. Braiding and measurement in these systems allow the topologically protected generation of the Clifford gates, which is not a computationally universal gate set. To make these systems universal quantum computers, it is sufficient to supplement the gate set with a “θ/2-phase gate”, R(θ) =diag[1, eiθ](where diag[1, eiθ] represents a 2×2 matrix in which off diagonal elements are zero (r12=r21=0) and elements r11=1 and r22=eiθ) (in some instances, R(θ) may be written as R(θ)), withθ ≠nπ/2(for n an interger). A particularly propitious choice for this is to use the π/8-phase gate, T =R(π/4), which can be generated if one has a supply of prepared or “magic states,” such as
                B              π        4              〉    =                    cos        ⁡                  (                      π            8                    )                    ⁢                      0        〉              -                  ⅈsin        ⁡                  (                      π            8                    )                    ⁢                                  1          〉                .            This is an advantageous choice because it is known how to “distill” magic states, i.e. produce a higher fidelity state from several noisy copies of the state, using only Clifford operations, for a remarkably high error threshold of approximately 0.14 for the noisy states.